/**
* Copyright (C) 2011 - present by OpenGamma Inc. and the OpenGamma group of companies
*
* Please see distribution for license.
*/
package com.opengamma.analytics.financial.model.finitedifference;
import static org.testng.AssertJUnit.assertEquals;
import java.util.Arrays;
import org.testng.annotations.Test;
import com.opengamma.analytics.financial.model.finitedifference.applications.CoupledPDEDataBundleProvider;
import com.opengamma.analytics.financial.model.finitedifference.applications.TwoStateMarkovChainDataBundle;
import com.opengamma.analytics.financial.model.interestrate.curve.ForwardCurve;
import com.opengamma.analytics.financial.model.interestrate.curve.YieldAndDiscountCurve;
import com.opengamma.analytics.financial.model.interestrate.curve.YieldCurve;
import com.opengamma.analytics.financial.model.option.pricing.analytic.formula.BlackFunctionData;
import com.opengamma.analytics.financial.model.option.pricing.analytic.formula.EuropeanVanillaOption;
import com.opengamma.analytics.financial.model.volatility.BlackImpliedVolatilityFormula;
import com.opengamma.analytics.math.curve.ConstantDoublesCurve;
import com.opengamma.analytics.math.function.Function1D;
import com.opengamma.util.test.TestGroup;
/**
* Test.
*/
@Test(groups = TestGroup.UNIT)
public class CoupledForwardFiniteDifferenceTest {
private static final CoupledPDEDataBundleProvider PDE_DATA_PROVIDER = new CoupledPDEDataBundleProvider();
private static final BlackImpliedVolatilityFormula BLACK_IMPLIED_VOL = new BlackImpliedVolatilityFormula();
private static BoundaryCondition LOWER1;
private static BoundaryCondition LOWER2;
private static BoundaryCondition UPPER;
private static final double SPOT = 0.03;
private static final double T = 5.0;
private static final double RATE = 0.04;
private static final ForwardCurve FORWARD = new ForwardCurve(SPOT, RATE);
private static final YieldAndDiscountCurve YIELD_CURVE = YieldCurve.from(ConstantDoublesCurve.from(RATE));
private static final double VOL1 = 0.15;
private static final double VOL2 = 0.70;
private static final double LAMBDA12 = 0.3;
private static final double LAMBDA21 = 4.0;
private static final double PROB_STATE1 = 1.0;
private static final Function1D<Double, Double> INITIAL_COND1;
private static final Function1D<Double, Double> INITIAL_COND2;
private static final boolean ISCALL = true;
static {
final Function1D<Double, Double> strikeZeroPrice1 = new Function1D<Double, Double>() {
@SuppressWarnings({"synthetic-access", "unused" })
@Override
public Double evaluate(final Double t) {
if (ISCALL) {
return probState1(LAMBDA12, LAMBDA21, PROB_STATE1, t) * SPOT;
}
return 0.0;
}
};
final Function1D<Double, Double> strikeZeroPrice2 = new Function1D<Double, Double>() {
@SuppressWarnings({"synthetic-access", "unused" })
@Override
public Double evaluate(final Double t) {
if (ISCALL) {
return (1 - probState1(LAMBDA12, LAMBDA21, PROB_STATE1, t)) * SPOT;
}
return 0.0;
}
};
LOWER1 = new DirichletBoundaryCondition(strikeZeroPrice1, 0.0);
LOWER2 = new DirichletBoundaryCondition(strikeZeroPrice2, 0.0);
//LOWER = new FixedSecondDerivativeBoundaryCondition(0, 0, true);
if (ISCALL) {
//UPPER = new DirichletBoundaryCondition(0, 6.0 * SPOT * Math.exp(T * RATE));
UPPER = new NeumannBoundaryCondition(0, 10.0 * SPOT * Math.exp(T * RATE), false);
//UPPER = new FixedSecondDerivativeBoundaryCondition(0, 6.0 * SPOT * Math.exp(T * RATE), false);
// UPPER = new NeumannBoundaryCondition(0.0, 10.0 * SPOT * Math.exp(T * RATE), false);
} else {
UPPER = new NeumannBoundaryCondition(1.0, 5.0 * SPOT * Math.exp(T * RATE), false);
}
INITIAL_COND1 = new Function1D<Double, Double>() {
@Override
public Double evaluate(Double x) {
return PROB_STATE1 * Math.max(0, SPOT - x);
}
};
INITIAL_COND2 = new Function1D<Double, Double>() {
@Override
public Double evaluate(Double x) {
return (1.0 - PROB_STATE1) * Math.max(0, SPOT - x);
}
};
}
@Test(enabled = false)
public void testMCSmile() {
final int timeNodes = 51;
final int spaceNodes = 151;
final MeshingFunction timeMesh = new ExponentialMeshing(0.00, T, timeNodes, 7.5);
final MeshingFunction spaceMesh = new HyperbolicMeshing(LOWER1.getLevel(), UPPER.getLevel(), SPOT, spaceNodes, 0.01);
// MeshingFunction spaceMesh = new ExponentialMeshing(SPOT / 10., SPOT * 5, spaceNodes, 0.0);
final double[] expiries = Arrays.copyOfRange(timeMesh.getPoints(), 0, timeNodes);
final double[] strikes = spaceMesh.getPoints();
final double[] forwards = new double[timeNodes];
final double[] df = new double[timeNodes];
for (int i = 0; i < timeNodes; i++) {
df[i] = YIELD_CURVE.getDiscountFactor(expiries[i]);
forwards[i] = SPOT / df[i];
}
final MarkovChain mc = new MarkovChain(VOL1, VOL2, LAMBDA12, LAMBDA21, PROB_STATE1);
double impVol;
final double weight = Math.exp(-LAMBDA12 * 0.004);
double[][] mcSims = mc.simulate(expiries, 10000, 0.0, weight);
final double[][] pricesA = mc.price(forwards, df, strikes, expiries, mcSims);
mcSims = mc.simulate(expiries, 1000, weight, 1.0);
final double[][] pricesB = mc.price(forwards, df, strikes, expiries, mcSims);
for (int i = 0; i < spaceNodes; i++) {
System.out.print("\t" + strikes[i]);
}
System.out.print("\n");
for (int j = 0; j < timeNodes; j++) {
final BlackFunctionData data = new BlackFunctionData(forwards[j], df[j], 0.0);
System.out.print(expiries[j]);
for (int i = 0; i < spaceNodes; i++) {
try {
final EuropeanVanillaOption option = new EuropeanVanillaOption(strikes[i], expiries[j], true);
impVol = BLACK_IMPLIED_VOL.getImpliedVolatility(data, option, weight * pricesA[j][i] + (1 - weight) * pricesB[j][i]);
} catch (final Exception e) {
impVol = 0.0;
}
System.out.print("\t" + impVol);
}
System.out.print("\n");
}
}
@Test(enabled = false)
public void testApproxSmile() {
final int timeNodes = 11;
final int spaceNodes = 151;
final MeshingFunction timeMesh = new ExponentialMeshing(0, 0.04, timeNodes, 0.0);
// MeshingFunction spaceMesh = new HyperbolicMeshing(LOWER1.getLevel(), UPPER.getLevel(), SPOT, spaceNodes, 0.1);
final MeshingFunction spaceMesh = new ExponentialMeshing(SPOT / 10., SPOT * 5, spaceNodes, 0.0);
final double[] expiries = Arrays.copyOfRange(timeMesh.getPoints(), 0, timeNodes);
final double[] strikes = spaceMesh.getPoints();
final double[] forwards = new double[timeNodes];
final double[] df = new double[timeNodes];
for (int i = 0; i < timeNodes; i++) {
df[i] = YIELD_CURVE.getDiscountFactor(expiries[i]);
forwards[i] = SPOT / df[i];
}
final MarkovChainSmallTimeApprox mc = new MarkovChainSmallTimeApprox(VOL1, VOL2, LAMBDA12, LAMBDA21, PROB_STATE1);
double impVol;
for (int i = 0; i < spaceNodes; i++) {
System.out.print("\t" + strikes[i]);
}
System.out.print("\n");
for (int j = 0; j < timeNodes; j++) {
final BlackFunctionData data = new BlackFunctionData(forwards[j], df[j], 0.0);
System.out.print(expiries[j]);
for (int i = 0; i < spaceNodes; i++) {
final double price = mc.price(forwards[j], df[j], strikes[i], expiries[j]);
try {
final EuropeanVanillaOption option = new EuropeanVanillaOption(strikes[i], expiries[j], true);
impVol = BLACK_IMPLIED_VOL.getImpliedVolatility(data, option, price);
} catch (final Exception e) {
impVol = 0.0;
}
System.out.print("\t" + impVol);
}
System.out.print("\n");
}
}
@Test
public void testDegenerate() {
//NOTE vols equal
final TwoStateMarkovChainDataBundle mcData = new TwoStateMarkovChainDataBundle(VOL1, VOL1, LAMBDA12, LAMBDA21, PROB_STATE1);
final CoupledFiniteDifference solver = new CoupledFiniteDifference(0.55, true);
final ConvectionDiffusionPDE1DCoupledCoefficients[] pdeData = PDE_DATA_PROVIDER.getCoupledForwardPair(new ForwardCurve(SPOT, RATE), mcData);
final int tNodes = 50;
final int xNodes = 150;
final MeshingFunction timeMesh = new ExponentialMeshing(0, T, tNodes, 7.5);
final MeshingFunction spaceMesh = new HyperbolicMeshing(LOWER1.getLevel(), UPPER.getLevel(), SPOT, xNodes, 0.01);
//MeshingFunction spaceMesh = new ExponentalMeshing(LOWER1.getLevel(), UPPER.getLevel(), xNodes, 0.0);
final PDEGrid1D grid = new PDEGrid1D(timeMesh, spaceMesh);
final CoupledPDEDataBundle d1 = new CoupledPDEDataBundle(pdeData[0], INITIAL_COND1, LOWER1, UPPER, grid);
final CoupledPDEDataBundle d2 = new CoupledPDEDataBundle(pdeData[1], INITIAL_COND2, LOWER2, UPPER, grid);
final PDEResults1D[] res = solver.solve(d1, d2);
final PDEFullResults1D res1 = (PDEFullResults1D) res[0];
final PDEFullResults1D res2 = (PDEFullResults1D) res[1];
double t, k;
double price;
double impVol;
final double tMin = 0.03;
for (int j = 0; j < tNodes; j++) {
t = res1.getTimeValue(j);
if (t > tMin) {
final double rootT = Math.sqrt(t);
final double df = YIELD_CURVE.getDiscountFactor(t);
final BlackFunctionData data = new BlackFunctionData(SPOT / df, df, 0.0);
for (int i = 0; i < xNodes; i++) {
k = res1.getSpaceValue(i);
final double z = (Math.log(k / SPOT) - (RATE - VOL1 * VOL1 / 2) * t) / VOL1 / rootT;
if (z > -2.6 && z < 3.2) {
price = res1.getFunctionValue(i, j) + res2.getFunctionValue(i, j);
final EuropeanVanillaOption option = new EuropeanVanillaOption(k, t, ISCALL);
try {
impVol = BLACK_IMPLIED_VOL.getImpliedVolatility(data, option, price);
} catch (final Exception e) {
impVol = 0.0;
}
//System.out.println(t + "\t" + k);
assertEquals(VOL1, impVol, 5e-3);
}
}
}
}
}
@Test
public void testSmile() {
final CoupledFiniteDifference solver = new CoupledFiniteDifference(0.55, true);
final TwoStateMarkovChainDataBundle mcData = new TwoStateMarkovChainDataBundle(VOL1, VOL2, LAMBDA12, LAMBDA21, PROB_STATE1);
final ConvectionDiffusionPDE1DCoupledCoefficients[] pdeData = PDE_DATA_PROVIDER.getCoupledForwardPair(FORWARD, mcData);
final int tNodes = 51;
final int xNodes = 151;
final MeshingFunction timeMesh = new ExponentialMeshing(0, T, tNodes, 7.5);
final MeshingFunction spaceMesh = new HyperbolicMeshing(LOWER1.getLevel(), UPPER.getLevel(), SPOT, xNodes, 0.01);
//MeshingFunction spaceMesh = new ExponentalMeshing(LOWER1.getLevel(), UPPER.getLevel(), xNodes, 0.0);
final double[] expiries = Arrays.copyOfRange(timeMesh.getPoints(), 1, tNodes);
final double[] strikes = spaceMesh.getPoints();
final double[] forwards = new double[tNodes - 1];
final double[] df = new double[tNodes - 1];
for (int i = 0; i < tNodes - 1; i++) {
df[i] = YIELD_CURVE.getDiscountFactor(expiries[i]);
forwards[i] = SPOT / df[i];
}
final MarkovChain mc = new MarkovChain(VOL1, VOL2, LAMBDA12, LAMBDA21, PROB_STATE1);
final double[][] mcSims = mc.simulate(expiries, 1000);
final double[][] mcPrices = mc.price(forwards, df, strikes, expiries, mcSims);
final PDEGrid1D grid = new PDEGrid1D(timeMesh, spaceMesh);
final CoupledPDEDataBundle d1 = new CoupledPDEDataBundle(pdeData[0], INITIAL_COND1, LOWER1, UPPER, grid);
final CoupledPDEDataBundle d2 = new CoupledPDEDataBundle(pdeData[1], INITIAL_COND2, LOWER2, UPPER, grid);
final PDEResults1D[] res = solver.solve(d1, d2);
final PDEFullResults1D res1 = (PDEFullResults1D) res[0];
final PDEFullResults1D res2 = (PDEFullResults1D) res[1];
double t, k;
double price;
double impVol, mcImpVol = 0;
final double tMin = 0.5;
final double zMax = 2.0;
double mcPrice;
for (int j = 1; j < tNodes; j++) {
t = res1.getTimeValue(j);
if (t > tMin) {
final double rootT = Math.sqrt(t);
final BlackFunctionData data = new BlackFunctionData(forwards[j - 1], df[j - 1], 0.0);
for (int i = 0; i < xNodes; i++) {
k = res1.getSpaceValue(i);
final double z = (Math.log(k / SPOT) - (RATE - VOL1 * VOL1 / 2) * t) / VOL1 / rootT;
if (Math.abs(z) < zMax) {
price = res1.getFunctionValue(i, j) + res2.getFunctionValue(i, j);
mcPrice = mcPrices[j - 1][i];
// System.out.println(t + "\t" + k);
assertEquals(mcPrice, price, 1e-1 * mcPrice);
final EuropeanVanillaOption option = new EuropeanVanillaOption(k, t, ISCALL);
try {
impVol = BLACK_IMPLIED_VOL.getImpliedVolatility(data, option, price);
mcImpVol = BLACK_IMPLIED_VOL.getImpliedVolatility(data, option, mcPrice);
} catch (final Exception e) {
impVol = 0.0;
}
assertEquals(impVol, mcImpVol, 4e-3);
}
}
}
}
}
@Test(enabled = false)
public void testSmilePrint() {
//final boolean print = true;
final CoupledFiniteDifference solver = new CoupledFiniteDifference(0.55, true);
final TwoStateMarkovChainDataBundle mcData = new TwoStateMarkovChainDataBundle(VOL1, VOL2, LAMBDA12, LAMBDA21, PROB_STATE1);
final ConvectionDiffusionPDE1DCoupledCoefficients[] pdeData = PDE_DATA_PROVIDER.getCoupledForwardPair(FORWARD, mcData);
final int tNodes = 51;
final int xNodes = 151;
//final double lowerMoneyness = 0.0;
//final double upperMoneyness = 3.0;
// MarkovChain mc = new MarkovChain(VOL1, VOL2, lambda12, lambda21, 1.0);
// double[] mcSims = mc.simulate(T, 10000); // simulate the vol path
final MeshingFunction timeMesh = new ExponentialMeshing(0, T, tNodes, 7.5);
final MeshingFunction spaceMesh = new HyperbolicMeshing(LOWER1.getLevel(), UPPER.getLevel(), SPOT, xNodes, 0.01);
//MeshingFunction spaceMesh = new ExponentialMeshing(LOWER1.getLevel(), UPPER.getLevel(), xNodes, 0.0);
final PDEGrid1D grid = new PDEGrid1D(timeMesh, spaceMesh);
final CoupledPDEDataBundle d1 = new CoupledPDEDataBundle(pdeData[0], INITIAL_COND1, LOWER1, UPPER, grid);
final CoupledPDEDataBundle d2 = new CoupledPDEDataBundle(pdeData[1], INITIAL_COND2, LOWER2, UPPER, grid);
final PDEResults1D[] res = solver.solve(d1, d2);
final PDEFullResults1D res1 = (PDEFullResults1D) res[0];
final PDEFullResults1D res2 = (PDEFullResults1D) res[1];
double t, k;
double price;
double impVol;
//final double lowerK, upperK;
//final double tMin = 0.02;
//Combined price
for (int i = 0; i < xNodes; i++) {
System.out.print("\t" + res1.getSpaceValue(i));
}
System.out.print("\n");
for (int j = 0; j < tNodes; j++) {
t = res1.getTimeValue(j);
//final double p1 = probState1(LAMBDA12, LAMBDA21, 1.0, t);
final double df = YIELD_CURVE.getDiscountFactor(t);
final BlackFunctionData data = new BlackFunctionData(SPOT / df, df, 0.0);
System.out.print(t);
for (int i = 0; i < xNodes; i++) {
k = res1.getSpaceValue(i);
price = res1.getFunctionValue(i, j) + res2.getFunctionValue(i, j);
final EuropeanVanillaOption option = new EuropeanVanillaOption(k, t, ISCALL);
try {
impVol = BLACK_IMPLIED_VOL.getImpliedVolatility(data, option, price);
} catch (final Exception e) {
impVol = 0.0;
}
System.out.print("\t" + impVol);
}
System.out.print("\n");
}
System.out.print("\n");
}
private static double probState1(final double lambda12, final double lambda21, final double pState1T0, final double t) {
final double sum = lambda12 + lambda21;
if (sum == 0) {
return pState1T0;
}
final double pi1 = lambda21 / sum;
return pi1 + (pState1T0 - pi1) * Math.exp(-sum * t);
}
}